[Turkmath:234] MSGSU Seminer: Mohan Ravichandran/ Interlacing polynomials, Ramanujam graphs and the Kadison-Singer problem/ 19.02.2015 16:00

[Emrah Çakçak]

Değerli liste üyeleri,

MSGSÜ Matematik Bölümü Genel Seminerleri, bu dönem Mohan Ravichandran'ın
konuşmasıyla başlıyor. Konuşmanın detayları aşağıda.

İyi çalışmalar,

Emrah Çakçak

--------------------------------------------------------------

Konuşmacı: Mohan Ravichandran (MSGSÜ)

Başlık: Interlacing polynomials, Ramanujam graphs and the Kadison-Singer
problem

Özet: I will talk about recent work of Adam Marcus, Daniel Spielman and
Nikhil Srivastava(MSS) where they use ideas from combinatorics and spectral
graph theory to settle several important problems in computer science and
mathematics. Two of these are constructions of Ramanjuan graphs(expander
graphs with the best possible expansion constants) and a solution of the
famous Kadison-Singer problem.

Ramanujan graphs were first constructed by Lubotzy, Philips and Sarnak and
independently by Margulis using deep ideas from number theory and geometric
group theory respectively. MSS provided a new construction in 2013, using
more or less elementary ideas, a construction that further removes
important numerical restrictions in all prior work.

The Kadison-Singer problem was one of the thorniest problems in operator
algebras till it was settled by this trio, also in 2013. The problem is
further related to dozens of problems in areas as disparate as C* algebras,
signal processing and harmonic analysis. Notably, a majority of the
mathematical community expected a negative solution to the problem, an
expectation that was confounded by Marcus, Spielman and Srivastava.
The techniques of their proofs are both remarkably elementary, requiring
little more than linear algebra and extremely powerful. I expect to even be
able to sketch their proofs within the time allocated to the talk.

Zaman: 19 Şubat 2015 (Perşembe),  16:00

Yer: MSGSÜ, Bomonti Kampüsü (Harita <http://math.msgsu.edu.tr/iletisim.html>),
Matematik Bölümü Seminer Odası.
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